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Oct13
EVENT DETAILS
lessTitle: Fast Direct Solvers for Boundary Integral Equations
Speaker: Dr. Adrianna Gillman, University of Colorado Boulder
Abstract: The numerical solution of linear boundary values problems play an important role in the modeling of physical phenomena.
As practitioners continue to want to solve more complicated problems, it is important to develop robust and efficient numerical methods. For some linear boundary value problems, it is possible to recast the problem as a boundary integral equation which sometimes leads to a reduction in dimensionality. The trade-off for the reduction in dimensionality is the need to solve a dense linear system. Inverting the dense N by N matrix via Gaussian elimination has a computational cost of O(N^3). When N is large, the cost in both memory and computational resources is too high for most practitioners. This talk presents solution techniques that exploit the physics in the boundary integral equation to invert the dense matrix for a cost that scales linearly (or nearly linearly) with N with
small constants. For example, on a laptop computer, a matrix with N=100,000 can be inverted in 90 seconds and applying the solver takes under a tenth of a second. The speed in which new boundary conditions can be processed makes these methods ideal applications involving many solves such as optimal design and inverse scattering. In these applications, fast direct solvers observe hundreds of times speed up over previously state of the art techniques. Examples of how these techniques can be used to create accelerated solvers for problems where the linear scaling solver is excessive will also be presented.
Bio: Adrianna Gillman is an Associate Professor in the Department of Mathematics at the University of Colorado, Boulder. In 2018, she was awarded an Alfred P. Sloan Research Fellowship. Her work has been supported by industrial contracts, NSF and, most recently, the Knut and Alice Wallenberg Foundation Grant, in cooperation with the Royal Swedish Academy of Sciences. Gillman’s research lies in the intersection of numerical linear algebra and numerical partial differential equations with an emphasis on developing high order discretizations and efficient solvers for the linear systems that result from these discretizations. Her work has been applied to applications including scattering and Stokes flow.
Zoom: https://northwestern.zoom.us/j/96310557268
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TIME Tuesday, October 13, 2026 at 11:00 AM - 12:00 PM
LOCATION M416, Technological Institute map it
CONTACT Natalie Masini natalie.masini@northwestern.edu EMAIL
CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)
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Oct27
EVENT DETAILS
lessTitle: Advances in Asymptotic and Computational Methods for Biological Transport
Speaker: Dr. Alan Lindsay, University of Notre Dame
Abstract: Asymptotic analysis remains one of the most powerful analytical tools for extracting interpretable information from mathematical models in science. These methods systematically exploit multiscale structure to reduce complex and often intractable problems to a sequence of tractable sub-problems. When coupled with modern numerical methods, they greatly expand the range and scope of scientific questions that can be addressed.
In this talk I will discuss the insights these tools have yielded into the role that geometry, dynamics and localization play in biological transport. For the diffusive delivery of cargoes to small reactive sites, they give precise information on how the spatial organization of those sites shapes function. This has led to new solutions to the long-standing Berg-Purcell problem and the narrow escape problem. Underpinning these results is a suite of high-order boundary integral solvers which pair with asymptotic methods to resolve multiscale features and massively expand the geometric scope of biological problems that can be investigated. Throughout the talk I will highlight where interactions with experimental science have guided the direction of the mathematics, and I will close with promising directions for future enquiry.
Zoom: https://northwestern.zoom.us/j/98486002568
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TIME Tuesday, October 27, 2026 at 11:00 AM - 12:00 PM
LOCATION M416, Technological Institute map it
CONTACT Natalie Masini natalie.masini@northwestern.edu EMAIL
CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)
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Nov24
EVENT DETAILS
lessTitle: Symmetry Breaking, Directed Movement, and Organized Tissue Response from Local Interactions
Speaker: Dr. Calina Copos, Northeastern University
Abstract: Pattern formation and symmetry breaking have long been areas of interest in applied mathematics. In living systems, these questions take on additional complexities: molecular interactions generate dynamic intracellular structures, individual cells develop persistent migratory behaviors, and populations of cells coordinate their dynamics to produce spatiotemporal patterns. A central question is how do biological systems break symmetry, select among competing dynamical states, and coordinate response across scales?
Using cell doublets as the smallest nontrivial collective unit, I will discuss mathematical models, computational methods, and dynamical systems approaches for investigating how local feedback, geometry, and confinement shape these collective dynamical states. We examine how mechanochemical interactions generate directional and coordinated migration, biases, and how nonlinear feedback and spatial coupling give rise to coherent oscillations, traveling waves, and other patterns. Extending these principles to larger cell clusters and tissues reveals emergent organization with implications for development, wound healing, and limb regeneration. These examples illustrate how mathematical models can bridge scales and uncover principles by which local interactions generate global organization.
Bio: Calina Copos is an Assistant Professor of Mathematics and Biology at Northeastern University. Her research group is broadly interested in mathematical biology and numerical and computational methods for PDEs, with a particular focus on the cell cytoskeleton and cell migration in tissue development, homeostasis, and regeneration. Prof. Copos received her Ph.D. in Applied Mathematics at University of California, Davis and did her postdoctoral work at the Courant Institute at New York University.
Zoom: https://northwestern.zoom.us/j/94290664465
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TIME Tuesday, November 24, 2026 at 11:00 AM - 12:00 PM
LOCATION M416, Technological Institute map it
CONTACT Natalie Masini natalie.masini@northwestern.edu EMAIL
CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)
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Dec12
EVENT DETAILSmore info
lessThe ceremony will take place on Saturday, December 12 in Pick-Staiger Concert Hall, 50 Arts Circle Drive.
TIME Saturday, December 12, 2026 at 4:00 PM - 6:00 PM
LOCATION Pick-Staiger Concert Hall map it
CONTACT Andi Joppie andi.joppie@northwestern.edu EMAIL
CALENDAR McCormick School of Engineering and Applied Science